hmmm .... good question.
After living in Japan for almost 10 years I still have trouble with them at times.
Way back when I just game up struggling with them and decided to allow myself be corrected. If you're not in a situation where you can practice "live Japanese" then it's going to be uch more difficult.
Thinking about this some more, I think I started using more and more properly was when I stopped using them as words and started using them as grammar markers (pointers, dividers ... )
watashi "ha" <--- subject designator
kare "ga" <--- object marker
e / ni <--- direction marker
I'm still horrible at grammar but slowly I got the feel for them.
Listening also helps.
You'll notice them with more and more practice.
You'll also notice where and when they're being used and not used.
I suck at particles, too, but there is an excellent book available on Amazon.com or Barnes and Noble (or your favorite book store) called, "All About Particles" by Naoko Chino. She has another book that I am working on right now that is written all in Japanese. It's called "Gaikokujin no tame no joshi", but I'd say you'd have to be pretty good at Japanese to find and order it. For what it's worth, the title is this in Japanese:
It's missed out the other common particles such as: "kara" and the obvious "no"
I don't know about great tips for learning when to use them. I just kinda guess what it is most of the time (with the exception of "ga" and "wa" which are really confusing at times)
I think "wa," "no," "o," are pretty easy to remember. Sometimes I wonder when to use "ni" (which can be remembered as meaning "in" in English, which is appropriately "ni" spelt backwards)... but "ni arimasu" tend to go hand in hand a lot in common usage
I just tend to learn sentences and break them down, then learn the vocab and grammar. Kinda backwards, but it works for me. You should stick to whatever is easiest for you. I've only been studying for a few months now, but I'm pretty confident with using the particles except for "de" at times and "wa/ga." "Wa" and "ga" is a little harder to understand, but sometimes can be thought of as "the" and "a" in English, respectively
You'll just notice them the more you read and use them. I think learning a few sentences containing a particle and learning about what the particle means is the best way to do it. But like all things, there is only one thing that will make you improve... repetition
Particles are tricky and Im sure they must have caused problems for anyone who ever studied Japanese as a foreign language (apart maybe from Koreans, whose language I heard has similar concepts: anyone know if this is true?).
I think the main problem is that there is no equivalent concept in English. Maybe it's for this reason I find the best approach is to not try to assign equivalent English prepositions as much as possible.
For this reason I think the link above might not be that useful: you end up with so many English words that could equate to the particle that it all gets too confusing.
The approach that moyashi mentions above, i.e just remembering the function of the particle is best, I think. If you keep these ideas in mind whilst practising as many sentences (or reading as many) as possible things will become clearer. If you can practise in a school or with Japanese friends then after a while being corrected should gradually sort out mistakes.
The way of thinking which helped me was:
wa: marks the topic, used especially when introducing a new topic or contrasting
ga: marks subject/agent of verb
ni/e: marks direction (actually a pretty direct equivalent of English "to")
ni: marks place where something EXISTS
de: marks place where an action HAPPENS
wo: marks object of the verb
The main problems that got me were, for example: when to use de and ni to mark the place, but thinking about the difference between verbs of action and the existence verbs helped, e.g.
sensei wa seitou no mae NI imasu: the teacher is in front of the students
senseu wa seitou no mae DE utatte imasu: the teacher is singing in front of the students
(my wholehearted apologies for the lameness of the example sentences)
Im sure there are a few exceptions to these general ideas, one that confused me at first is best shown in the sentence "the plane is flying through/in the sky". At first I thought you should use "de" or "ni" but the correct one is "wo":
hikouki wa sora WO tonde imasu.
This applies to all verbs of motion (walk, run, fly etc.) where the particle "wo" is used to mark the thing that is being travelled through. But you can still think of wo as just marking the subject of the verb, meaning a direct English equivalent of this Japanese would be "the plane is flying the sky" which isn't very natural English but we certainly can use phrases like "walk the street" or "sail the sea" in English, its just that in Japanese this type of thinking extends to all verbs of motion.
This is covered in the example sentences in the link given above in which the particle is equated to English 'through' 'in' etc. But if you consider the Japanese for "to walk in front of someone" we need wo for that, too:
hito no mae WO arukimasu
Or the phrase "walk along the street":
michi WO arukimasu
None of the English equivalents for "wo" given on this site cope with this situation, and to do so you'd just end up adding yet another English word (for example 'along') to the list and making it more daunting and less helpful to try and remember, so again I come back to reccommending the function-based approach to remembering that moyashi introduced above.
As Tom says, the difference between wa and ga is the most vague, though I noticed when I came to Japan that I was using "wa" far more often than Japanese people were, maybe it's because the first sentences we learn as beginners always use "wa" and I got into the habit of using it too much.
However you try to remember them the only way to get good is practise, especially via exposure to real Japanese and getting friends to correct you. I studied for 6 months in Japan and almost every day we had "fill in the particle" type questions and it didn't take long to go from hating these questions to actually being pretty confident about getting them right and being able to use them correctly most of the time.